Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C42 |
| prime radical, cosocle | C32×D52 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C3⋊(C3⋊#1042) | C4 | semidirect |
| 6. C5×C3⋊ΓL(1,𝔽16) | C4 | semidirect |
| 7. C32×#1044 | C4 | semidirect |
| 8. C32×#1043 | C4 | semidirect |
| 21. C3×#1044 | Dic3 | semidirect |
| 22. C3×#1043 | Dic3 | semidirect |
| 24. C32×C52 | C42 | semidirect |
| 29. C3⋊ΓL(1,𝔽16) | AGL(1,𝔽5) | semidirect |
| 42. #1044 | C3⋊Dic3 | semidirect |
| 43. #1043 | C3⋊Dic3 | semidirect |
| 51. C3×C52 | C4×Dic3 | semidirect |
| 66. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 79. C52 | C4×C3⋊Dic3 | semidirect |
| 94. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 104. C32 | AGL(1,𝔽5)2 | semidirect |
| 110. C5 | AGL(1,𝔽5)×C3⋊Dic3 | semidirect |
| 116. C3 | ΓL(1,𝔽16)⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C3⋊ΓL(1,𝔽16) | 2 |
| C32×D5⋊AGL(1,𝔽5) | 2 |
| ΓL(1,𝔽16)⋊AGL(1,𝔽5) | 3 |
| AGL(1,𝔽5)×C3⋊Dic3 | 5 |